An apology would forestall the possibility of Turkish lawsuits against Israel after a United Nations report on the May 31, 2010, raid by Israeli commandos is released, Haaretz quoted Yehuda Weinstein as telling Netanyahu privately.
Israel's Justice Department had no immediate comment on the report. The newspaper did not say what Netanyahu's response to the recommendation was.
Weinstein argued Israel should consider apologizing for operational mistakes and the misuse of force in the raid on the Turkish ship Mavi Marmara, if Turkey promises not to file lawsuits against Israeli soldiers and officers, the newspaper said.
The suggested apology would be general and would not apply to stopping the Palestinian-aid flotilla or address calls for Israel to end its four-year blockade of the Gaza Strip, Haaretz said.
Israel bans direct shipments to Gaza.
The U.N. investigation, set to be published Wednesday, is expected to find the naval blockade legal but conclude the commandos used excessive force while intercepting the ship, Haaretz said. It mentions autopsy reports that claim the activists killed were shot several times.
The United States is concerned its release could hurt U.S. Middle East interests.
Israel said after the raid its troops had been attacked by passengers identified as Turkish Islamic militants who wielded knives, sticks and clubs, and the commandos fired only in self-defense. Seven Israelis were wounded in the confrontation.
The raid touched off a furor in Turkey and much of the Middle East, and intensified calls for Israel to end the blockade.
An Israeli investigation later found the killings were justified, even though the raid was plagued by errors of planning, intelligence and coordination.